I think this works:

--first part gets events within the date range

SELECTevt.*

FROM dbo.#Events evt

WHERE evt.ProcessDate BETWEEN @StartDate AND @EndDate

--second part gets related events that occurred before

UNION ALL

SELECTPrior.*

FROM (SELECT LinkRL4, MIN(ProcessDate) AS ProcessDate FROM dbo.#Events evt WHERE ProcessDate BETWEEN @StartDate AND @EndDate GROUP BY LinkRL4) AS MinDate

CROSS APPLY (

SELECT TOP 1 evt.*

FROM dbo.#Events evt

WHERE evt.LinkRL4 = MinDate.LinkRL4

AND evt.ProcessDate < MinDate.ProcessDate

ORDER BY evt.ProcessDate DESC) as Prior

ORDER BY LinkRL4, ProcessDate, L4Ident